This lecture covers the basics of core concepts in probability and statistics to be used in the course. These include random variables, continuous and discrete distributions, joint and conditional distributions, the chain rule, marginalization, Bayes Rule, independence and conditional independence, and expectation. Probability models are discussed along with the concepts of independently and id...

Abstract. Definitions from the theory of point processes are recalled. Models of intensity function paramaterization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the Hawkes (unidimensional andmultidimensional)process, Autoregressive Conditional Duration(ACD), and Log-ACD models. The Autoregressive Conditional Intensity model is a...

Abstract. We show what properties of the time series we can find by examining the behavior of the conditional quasi-likelihood function, even when the time series does not necessarily satisfy the model and is not necessarily Gaussian. We consider fitting a parametric model to a time series and obtain the maximum likelihood estimates of unknown parameters included in the model by regarding the t...

This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yiel...

This paper presents a quasi-conditional likelihood method for the consistent estimation of both continuous and count data models with excess zeros and unobserved individual heterogeneity when the true data generating process is unknown. Monte Carlo simulation studies show that our zero-inflated quasi-conditional maximum likelihood (ZI-QCML) estimator outperforms other methods and is robust to d...

Abstract. Definitions from the theory of point processes are recalled. Models of intensity function paramaterization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the Hawkes process, Autoregressive Conditional Duration(ACD), and Log-ACD models. The Autoregressive Conditional Intensity model is also discussed. Data from the symbol ...